Estimating the volumetric flow of rivers and streams is an important problem in resource management and flood control. One may survey the cross-channel bed depth to develop a cross-sectional profile, which is then divided into sections. Water velocities within each section are then sampled at multiple depths using a submersible velocity probe. In this way, the channel cross-section is divided into smaller areas, each of which is associated with a measured velocity. From this painstakingly collected data set, a total volumetric flow rate may be computed.
Collection of the required multi-point data is, at best, a time-consuming and costly process and, during conditions such as flooding, quite hazardous. Consequently, daily or hourly estimates often depend on measuring a single parameter such as river stage (e.g., a single-point water level) and correlating that with a rating curve developed through more rigorous measurements over time.
One cannot, in general, extrapolate the entire rating curve from a single river survey because the curve's slope depends on which hydrodynamic controls govern the river behavior at various water levels. For example, high water may cause some rocks or sand bars to become submerged, thus allowing significant changes in flow patterns. This means that the correct rating curve shape is often unknown at a particular stage, e.g., flood stage, and there is value in discharge estimation methods that do not depend on knowing the rating curve.
One method involves entropic flow modeling. This method provides an estimate of the cross-sectional average velocity that depends on the present maximum velocity and on a previously determined coefficient which is nearly independent of river stage. According to entropic flow modeling theory there is a site-dependent proportionality between the maximum velocity and the cross-sectional average velocity. In wide channels, the maximum velocity often occurs at the water surface, typically near the center of the channel.
If the river bed and bank shapes have been previously surveyed, then the relationship between water height and cross-sectional flow area is also known. It thus becomes possible to calculate discharge as average velocity multiplied by cross-sectional area, based only on two measurements: the water height and the maximum velocity. Moreover, water height and maximum surface velocity are measureable from a distance by so-called non-contact sensors. Examples of non-contact measurement sensors are ultrasonic distance sensors for water level and Doppler radar sensors for surface velocity. Non-contact level and velocity sensors are often mounted from bridges spanning the river or stream of interest. These sensors allow river or stream discharge to be estimated during flood stage at little risk to personnel because nothing needs to be put into the water.
An alternative method for measuring water height is a submerged pressure sensor, whose output will vary with its depth of submersion. An alternative for measuring velocity is a permanently installed ultrasonic current meter, typically mounted below the water line on a bridge pylon. Submerged sensors such as these require more frequent maintenance and are susceptible to damage during flood events. This is why non-contact sensors are preferable.
Some Ultrasonic level sensors are available, and some models are intended specifically for measuring river stage.